In this paper, we investigate a class of anisotropic initial-boundary
value problems, involving the Finsler-Laplacian. Firstly, by using a
first-order differential inequality technique, we provide some
appropriate conditions on the data which guarantee the blow-up of the
solution at some explicit finite time. Next, under different appropriate
conditions on the data, we will make use of a comparison principle to
prove the global boundedness of the solution. Finally, by using a
maximum principle for an appropriate P-function, in the sense of L.E.
Payne, we derive some explicit exponential time decay bounds for the
solution and its derivatives..